Question

The lodge at the Three Lakes Resort is offering the following two options for a holiday weekend.

Option 1: 3 nights including six meals for $132.00
Option 2: 3 nights including two meals for $109.00

At these rates, what is the cost of one night's lodging?

Answer 1

Change each sentence into an algebraic equation.

3N+6M=132
3N+2M=109

Answer 2

Of course, you have to assume the nightly rate is the same and the per meal cost is the same.

Answer 3

Using the first equation:

3N=132-6M
N=(132-6M)/3

Substitute into the second equation, the value of N

3(132-6M)/3 + 2M = 109
132-6M+2M=109
4M=23
M=5.75

Substitute the value M into either equation:

3N+2(5.75)=109
3N=109-11.50
3N=97.50
N=32.50

Answer 4

or we could reason as follows: since the nights are the same you know that 4 meals cost
$132-$109=$23
therefore two meals cost $11.5 (rather cheap) and so 3 nights cost $109-$11.5=$97.50 and so one night cost $32.50